A theoretical method is presented for determining molecular hyper-magnetizabilities and magnetic shielding polarizabilities to first order in a perturbing electric field. The procedure is based on formal annihilation of either diamagnetic or paramagnetic contributions to the quantum mechanical electron current density, via a continuous transformation of its origin all over the molecular domain. Analytical expressions for the third-rank tensors are obtained, which, in the limit of exact eigenfunctions to a model Hamiltonian, reduce to the conventional terms. They can also be expressed as the expectation value of certain commutators over the reference electronic state. In any calculation relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed, all the components of the magnetic shielding polarizability evaluated within these methods are origin independent, and the constraints for charge and current conservation are exactly satisfied. On the other hand, the hypermagnetizability depends linearly on the origin of the vector potential.

A theoretical method is presented for determining molecular hyper-magnetizabilities and magnetic shielding polarizabilities to first order in a perturbing electric field. The procedure is based on formal annihilation of either diamagnetic or paramagnetic contributions to the quantum mechanical electron current density, via a continuous transformation of its origin all over the molecular domain. Analytical expressions for the third-rank tensors are obtained, which, in the limit of exact eigenfunctions to a model Hamiltonian, reduce to the conventional terms. They can also be expressed as the expectation value of certain commutators over the reference electronic state. In any calculation relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed, all the components of the magnetic shielding polarizability evaluated within these methods are origin independent, and the constraints for charge and current conservation are exactly satisfied. On the other hand, the hypermagnetizability depends linearly on the origin of the vector potential.